A polygon is a flat, two-dimensional shape that is formed by connecting a finite number of straight line segments. The points where the line segments meet are called vertices, and the line segments themselves are known as edges or sides.
Polygons are classified based on the number of sides they have:
- Triangle: A polygon with three sides.
- Quadrilateral: A polygon with four sides.
- Pentagon: A polygon with five sides.
- Hexagon: A polygon with six sides.
- Heptagon: A polygon with seven sides.
- Octagon: A polygon with eight sides.
Polygons can also be categorized as regular or irregular:
- Regular polygons have all sides and angles equal. Examples include an equilateral triangle and a square.
- Irregular polygons have sides and angles that are not all equal. For instance, a scalene triangle is irregular.
In addition to their sides and angles, polygons can also be classified as convex or concave:
- Convex polygons have all interior angles less than 180 degrees, which means that no line segment drawn between any two points inside the polygon will extend outside the polygon.
- Concave polygons have at least one interior angle greater than 180 degrees, and there exists at least one line segment connecting two points inside the polygon that extends outside of it.
Understanding polygons is fundamental in geometry, as they appear in various real-world applications, from architecture to graphic design. Visualizing them helps in grasping their properties and applying them to solve problems in mathematics.